When trying to solve a pde using Laplace transform, I need to invert an expression of the form(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{\exp{(-as-b\sqrt{s})}}{s^2}[/tex]

A friend told me that Mathematica cannot invert such expression. I try using convolution but a bit loss when trying to evaluate the integral of Erfc(.).

[tex]L^{-1}\{\frac{\exp{(-as-b\sqrt{s})}}{s^2} \}[/tex]

[tex]=L^{-1} \{ \frac{e^{-as}}{s} \} * L^{-1} \{ \frac{e^{-b\sqrt{s}}}{s} \} [/tex]

[tex]=H(t-a) * Erfc(\frac{b}{2\sqrt{t}}\) [/tex]

[tex]=\int_0^t H(t-\tau-a) Erfc(\frac{b}{2\sqrt{\tau}}\) d\tau[/tex]

How do we proceed from here?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Laplace Inversion

**Physics Forums | Science Articles, Homework Help, Discussion**